Question

You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in six equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won —assuming annual interest rate of 9.50%.

Answer 1

Answer:

$31615648

Explanation:

The annual amount that I would receive = $35,000,000 / 6 = $5,833,333

There are 6 annual payments that I will receive, one of them is to be received today so its should not be discounted as $1 today is worth $1 today but after a passage of time would not be $1, it might be worth $0.9.

So

Present Value =   Cash flow  *  1 / (1+r)^n

Remember that r is the discount rate  and n is the number of years.

Y0 PV =  $5,833,333  

Y1 PV =   $5,833,333 * 1/(1+9.5%)^1 = $5327245

Y2 PV =  $5,833,333 * 1/(1+9.5%)^2 = $4865064

Y3 PV =  $5,833,333 * 1/(1+9.5%)^3 = $4442981

Y4 PV =  $5,833,333 * 1/(1+9.5%)^4 = $4057517

Y5 PV =  $5,833,333 * 1/(1+9.5%)^5 = $3705495

Y6 PV =  $5,833,333 * 1/(1+9.5%)^6 = $3384013

Present Value of Lottery = (Y0 PV + Y1 PV + Y2 PV + Y3 PV + Y4 PV +Y5 PV + Y6 PV)

Present Value of Lottery = $5,833,333 + $5327245 + $4865064 + $4442981 + $4057517 + $3705495 + $3384013 = $31615648

So this is the amount that I will receive in todays value.